code: def log_marginal(
      self,
      observations: Tensor,
      function_dist: MultivariateNormal,
      *args: Any,
      **kwargs: Any,
  ) -> Tensor:
      likelihood_samples = self._draw_likelihood_samples(
          function_dist, *args, **kwargs
      )
      log_probs = likelihood_samples.log_prob(observations)
      res = log_probs.sub(math.log(log_probs.size(0))).logsumexp(dim=0)
      return res
  
imports: import math
  import warnings
  from abc import ABC, abstractmethod
  from copy import deepcopy
  from typing import Any, Dict, Optional, Union
  import torch
  from torch import Tensor
  from torch.distributions import Distribution
  from ..None import settings
  from ..distributions import base_distributions, MultivariateNormal
  from ..module import Module
  from ..utils.quadrature import GaussHermiteQuadrature1D
  from ..utils.warnings import GPInputWarning
label_desc: Use image node_id 6 for calling the _Likelihood obj's underlying member method code with example usage: obj.log_marginal(observations, function_dist) and returns: res